Which of the following numbers is a multiple of 11? ${67,74,94,110,115}$
Solution: The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $67 \div 11 = 6\text{ R }1$ $74 \div 11 = 6\text{ R }8$ $94 \div 11 = 8\text{ R }6$ $110 \div 11 = 10$ $115 \div 11 = 10\text{ R }5$ The only answer choice that leaves no remainder after the division is $110$ $ 10$ $11$ $110$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $110$ $110 = 2\times5\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $110$. We can say that $110$ is divisible by $11$.